Since carbon fibre composites only seem to have about half the Young's modulus of steel, they would be rather bendy. Lightness wouldn't be much of an advantage except, maybe, in the International Space Station (Images of Dean, Smith and Grace with beryllium bed :-).
Tungsten is twice as stiff as steel and is used to make tool holders for lathes using ceramic inserts.... Think 75hp going into an 8" diameter super alloy workpiece. Tungsten carbide is nearly 3.5 times as stiff as steel and is used for boring pars.
Hey grandma, do you know how to suck eggs?
Mark Rand RTFM